Honestly, RWBY's emotional palette is so defined by its tone that I think Grimms struggle by default. The show frames them as forces of nature, not characters with interiority. A Grimm feeling conflicted goes against the fundamental rules—they're embodiments of destruction and negativity.
That said, the most interesting angle I've seen writers take isn't internal conflict for the Grimm itself, but conflict generated through it. An OC who can control or influence Grimms, even partially, creates immediate, raw emotional stakes. Their power is a direct conduit for the world's negativity, and every use risks losing control or corrupting them. The conflict isn't the Grimm's feelings; it's the human(ish) character's horror at their own connection to it. Watching a controlled Grimm tear into something while they're desperately trying to rein it back in? That's where the emotional weight lands.
I once read a fic where an OC's Semblance was 'empathy' with Grimms, feeling their mindless hunger. They had to constantly fight the urge to give in, which isolated them completely. The real drama came from other characters misreading their withdrawal as coldness.
For a pure Grimm OC, you'd almost have to build a new mythology around it being an anomaly. Maybe it gained a fragment of a lost soul, or was born from a uniquely paradoxical emotion. But then you're writing an original fantasy creature wearing RWBY's skin, which can work if you're upfront about it.